Similarity Continua and Criteria in Memetic Theory and Analysis

The aim of this article is to schematize and quantify certain of the similarity relationships which are relevant to the application of memetics to music, in order to sketch a methodology by which evolutionarily significant resemblances (particularly in the melodic dimension) might be evaluated. The degree of similarity between two musical patterns is central in memetics, because the determination of whether homology (similarity resulting from replication), as opposed to analogy (similarity arising fortuitously), is operative in particular transmission situations often hinges upon it. After outlining David Cope’s five categories of melodic similarity and relating them to memetics, the Earth-Mover’s Distance (EMD) metric is discussed and its relevance to the psychological, evolutionary, and neurobiological aspects of similarity is evaluated. It is argued that the EMD may be used to quantify both the perceptual-cognitive salience intrinsic to musemes, and the effort required in mutating a museme from a “source” (evolutionarily earlier) to a “copy” (evolutionarily later) form, the latter understood as an index of similarity. These ideas are brought together by means of an analysis of a short passage from the finale of Beethoven’s Piano Sonata op. 106 (“Hammerklavier”), which applies various weighting schemes to the EMD calculations.